Study on the Signal Processing System of Rhodium Self-Powered Neutron Detectors and Neutron Sensitivity Reactor Testing

Jing Peng¹, Zhiqi Guo²,³, Jianxiong Shao²

¹ Chengdu Textile College, Chengdu, Sichuan 611731, China
² School of Nuclear Science and Technology, Lanzhou University, Lanzhou, Gansu 730000, China
³ China Nuclear Power Research and Design Institute, Chengdu, Sichuan 610005, China

Abstract

Self-Powered Neutron Detectors (SPNDs) serve as critical components for measuring neutron flux within reactor cores. However, due to their unique response mechanisms, SPND signal currents are typically weak and exhibit significant time delays. Moreover, research on SPND sensitivity currently lacks experimental data obtained under actual in-pile conditions. This study focuses on rhodium self-powered neutron detectors (Rh-SPNDs) and addresses these challenges through two key innovations: the development of specialized amplification circuitry for weak current signals and the implementation of algorithmic processing to compensate for delayed responses. These advances culminated in a fast-response Rh-SPND system that reduced the detector's signal response time from several hundred seconds to approximately 3 seconds. Comprehensive irradiation tests were subsequently conducted on the Rh-SPNDs in the Minjiang Test Reactor (MJTR). The experimental results demonstrate that as reactor power increased progressively, the temperature in the test section rose correspondingly, stabilizing at 42.4°C during full-power operation. The output current of the Rh-SPNDs increased with reactor power, with consistently higher currents measured on the "sunny side" (facing the core) compared to the "shady side" (facing away from the core). Based on these measurements, the thermal neutron sensitivity of the Rh-SPNDs was calculated, yielding values of 1.66×10⁻²⁰/A·(n·cm⁻²·s⁻¹)⁻¹, 1.68×10⁻²⁰/A·(n·cm⁻²·s⁻¹)⁻¹, and 1.44×10⁻²⁰/A·(n·cm⁻²·s⁻¹)⁻¹ for the three detectors tested.

Keywords: SPND; Fast response; In-pile testing; Neutron sensitivity

Classification Code: O571.53
Document Code: A

Introduction

On July 16, 2021, the International Atomic Energy Agency (IAEA) released the updated report International Status and Prospects of Nuclear Power [1], which outlines the current state and future prospects of nuclear power generation while emphasizing its role in mitigating climate change and achieving sustainable development. Neutron flux represents a critical physical parameter for nuclear reactors, holding significant importance for safe and stable reactor operation as well as real-time power monitoring [2]. Self-Powered Neutron Detectors (SPNDs) have emerged as essential instruments for in-core neutron flux measurement due to their compact size, simple structure, and self-powered operation without external power requirements. These detectors enable real-time mapping of neutron flux distributions and reflect core power profiles [3-5].

Research on SPND applications in reactor core nuclear instrumentation systems began in the former Soviet Union during the late 1950s and early 1960s, with subsequent development and deployment by the United States, Japan, South Korea, and other nations [6]. In 1972, Brakas M conducted in-pile tests on various SPND models in the Halden Boiling Water Reactor, accumulating extensive experience regarding sensitive element performance in nuclear reactor environments [7]. M.N. Baldwin measured detector response characteristics in a typical pressurized water reactor environment, establishing relationships with boron concentration and power density, and determined the relationship between rhodium wire diameter and beta emission rate by measuring currents from bare and cadmium-covered rhodium wires in a thermal neutron field [8]. O. Strindehag performed long-term testing on vanadium and cobalt detectors, reported fast-response experimental results for cobalt detectors, and documented experiences in power reactor flux detector assembly design, installation, and associated electronic circuitry and data processing systems [9]. W. Johnstone employed compensated conductors and differential amplifiers to measure SPND currents, utilizing inverse function amplifiers to predict the final values of slowly varying current amplifier outputs [10].

Among SPND materials, rhodium offers a larger neutron reaction cross-section compared to cobalt and vanadium, resulting in greater sensitivity currents. Consequently, rhodium self-powered neutron detectors (Rh-SPNDs) have become one of the most widely used SPND variants [11]. This paper investigates signal amplification and delay response compensation for Rh-SPNDs, proposing a discrete processing method based on step response invariance to mitigate time delay effects. Furthermore, in-pile irradiation tests were conducted on fabricated detectors in the Minjiang Test Reactor (MJTR) to perform neutron sensitivity consistency tests within irradiation channels, completing neutron flux measurements and determining the neutron sensitivity of Rh-SPNDs for the corresponding channels.

1.1 Basic Structure

A typical Rh-SPND structure is illustrated in [FIGURE:1], consisting of a probe and a sheathed signal cable. The probe serves as the detector's core component, comprising an emitter, insulator, and collector [12]. The emitter material is rhodium, representing the most critical part of the detector that determines its classification and fundamental performance. The insulator employs high-temperature resistant materials insensitive to neutrons, typically aluminum oxide or magnesium oxide, while the collector material utilizes Inconel [13].

1.2 Response Principle

The signal current in Rh-SPNDs comprises primarily prompt current and delayed current. As shown in [FIGURE:2], neutrons entering the detector undergo (n, γ) reactions with ¹⁰³Rh to produce ¹⁰⁴Rh and ¹⁰⁴ᵐRh. The (n, γ) reaction occurs instantaneously, with emitted gamma photons generating electrons through photoelectric, Compton, and electron-positron pair production effects in the emitter material. These electrons traverse the insulator to reach the collector, forming what is known as prompt current, which accounts for approximately 5-15% of the total current. The (n, γ) reaction with ¹⁰³Rh produces ¹⁰⁴ᵐRh with a 7.6% probability and ¹⁰⁴Rh with a 92.4% probability. The ¹⁰⁴ᵐRh isomer decays to ¹⁰⁴Rh with a half-life of 4.4 minutes, and the subsequent decay of ¹⁰⁴Rh emits electrons that form the delayed current, representing 85-95% of the total current [15].

Gamma rays from the reactor also generate currents in the detector, contributing approximately 5-8% of the total SPND current. This component constitutes an interference signal that cannot be electronically filtered based on response time or waveform characteristics since its generation mechanism mirrors that of the prompt current in Rh-SPNDs. Consequently, this contribution is typically calculated using Monte Carlo simulations or numerical methods to determine its magnitude and proportion, with algorithmic compensation applied in the backend electronics for correction.

2 Rh-SPND Signal Processing

The sensitivity of Rh-SPNDs, defined as the coefficient for converting output current to neutron flux, is given by [16]:

$$S = \frac{I}{\phi}$$

where $S$ denotes sensitivity, $I$ represents the total current, and $\phi$ indicates the neutron flux near the detector.

Rh-SPND output current signals exhibit several challenging characteristics: weak current intensity, high background noise, significant common-mode interference, and substantial time delays. Effective signal processing is therefore essential for practical detector application. This process involves signal amplification, conversion, and filtering to suppress noise and interference while enhancing signal clarity and accuracy. Processed signals are converted to digital form through a data acquisition system, after which host computer software performs further processing and correction using precise algorithms.

The signal processing system employs a multi-channel weak current amplifier featuring differential input capability and low-pass filtering functionality, with selectable measurement ranges. This system amplifies the detector's weak current signals and converts them into standard voltage signals suitable for sampling by AD modules while enabling remote transmission capabilities.

The design incorporates weak current amplifier and filter circuit modules alongside high-precision analog-to-digital conversion functional modules to achieve detector signal processing, data acquisition, and processing. The Rh-SPND output current signals undergo amplification, filtering, and interference suppression, with the weak electrical signals linearly converted to 0-10 V voltage signals. A 16-bit high-precision AD conversion module transforms these voltage signals into digital quantities, which are then processed, corrected, and converted by the host computer to obtain reactor neutron flux and power data for display, storage, and report generation. The processing flow is illustrated in [FIGURE:3].

2.1 Weak Current Amplification Module

The delayed signal from rhodium self-powered detectors consists primarily of two components. As shown in [FIGURE:2], ¹⁰⁴Rh has a half-life of 42 seconds, while ¹⁰⁴ᵐRh has a half-life of 4.4 minutes. Assuming a saturated maximum total current of 10⁻⁷ A that decays bi-exponentially according to equation (2), [FIGURE:4] demonstrates that after 10 minutes (600 seconds) of decay, the remaining current is 7.5×10⁻¹⁰ A, and after 20 minutes, the residual current is still 8.3×10⁻¹¹ A. Estimates indicate that under normal operating conditions, the detector current varies across three orders of magnitude from 10⁻¹⁰ to 10⁻⁷ A over extended periods. Therefore, an amplifier range covering three orders of magnitude suffices for practical engineering requirements.

$$I(t) = 10^{-7} \times (0.923 \times e^{-t/427} + 0.077 \times e^{-t/264})$$

To achieve weak current amplification, the high-performance DC operational amplifier LTC2063 was selected, featuring an offset voltage as low as 5 μV, temperature drift of merely ±0.03 μV·°C⁻¹, bias current of 0.5 pA, and open-loop gain up to 140 dB, thereby meeting the demands of weak current amplification.

The intense gamma field within the reactor core generates gamma currents in both the detector and sheathed transmission cables, while the high-temperature environment introduces thermal noise currents into the detector signals. These noise and interference currents become particularly pronounced when the detector output neutron current is weak, directly impacting measurement accuracy and reliability. Signal processing is therefore critical for effective detector application, requiring integrated electronic and data systems to adequately suppress background noise and common-mode interference currents for accurate extraction and detection of true neutron-sensitive currents.

The single-channel current amplifier is shown in [FIGURE:5]. The circuit comprises three amplification stages: an input stage using LTC2063, an intermediate gain adjustment stage employing OP07, and an output stage also utilizing OP07. The input stage adopts a differential input configuration that effectively suppresses common-mode interference on the signal line through compensation conductors, implementing a transimpedance amplifier with feedback resistors ranging from 1 MΩ to 10 MΩ and low-frequency filtering at the output. The intermediate stage employs high-impedance relays to switch feedback resistors, enabling gain selection and stepped adjustment via the host computer as an inverting voltage amplifier with gains of 46 dB, 66 dB, and 106 dB. The output stage uses a voltage follower configuration for signal driving and filtering. The final current amplifier module achieves a current measurement range of -5.0 μA to +5.0 μA with ±1 nA accuracy, producing an output voltage range of -5 V to +5 V after current amplification.

2.2 Signal Processing Module

To ensure high precision during analog-to-digital conversion, Siemens S300 series analog input modules were selected for acquiring current and temperature signals, with the ATMEGA128 chip chosen as the microcontroller unit due to its stable performance and robust processing capabilities. Both ADC and DAC modules employ 16-bit resolution chips to maintain high accuracy throughout the signal conversion process.

The time delay effect in neutron current generated by the rhodium emitter is significant, with signal delays extending for several minutes. To enable real-time, rapid measurement of reactor thermal neutron flux variations, compensation processing is required for the Rh-SPND response current (spanning tens of minutes) to obtain output signals that can quickly follow neutron flux changes (within seconds). Current methods for eliminating delayed response include inverse function amplifier compensation, Kalman filtering, robust filtering, and H₂/H∞ hybrid filtering. [TABLE:1] compares the advantages and disadvantages of these approaches.

TABLE:1 Comparison of Signal Response Delay Elimination Methods

Delay Elimination Method Advantages Disadvantages Inverse Function Amplifier Filtering [17] Simple implementation Signal distortion issues Kalman Filtering [18] Reduces delay to 2-3 seconds, noise reduction Requires statistical noise information H₂/H∞ Hybrid Filtering [19] Reduces delay to 2-10 seconds Introduces excessive empirical tuning parameters Robust Filtering [20] Excellent noise suppression, fewer parameters May cause signal distortion, requires two empirical parameter values

To process these continuous signals, the continuous-time system governing them must be equivalently transformed into a discrete-domain system. Discretization maps the continuous-time system transfer function to a discrete-time system transfer function. This study employed four discretization methods: forward difference transformation, backward difference transformation, step response invariance, and bilinear transformation [21]. Using inverse function reconstruction for secondary signal processing, the system achieves rapid response within seconds while accurately tracking neutron flux rate changes. The characteristics of each method are summarized in [TABLE:2], with the step response invariance method proving optimal by reducing time delay to 2.8 seconds. Consequently, this method was adopted for Rh-SPND signal processing to minimize time delay effects. Laboratory test results for the developed fast-response module are shown in [FIGURE:6], where waveform 2 (lower) represents the detector's delayed response output with its characteristic long delay time, while waveform 4 (upper) shows the compensated algorithm output with significantly improved response time, reducing the detector's signal response from hundreds of seconds to approximately 3 seconds for step changes in neutron flux.

TABLE:2 Time Constant Results After Signal Processing with Different Algorithms

Algorithm First Processing Second Processing Forward Difference 29.4 s 29.4 s Backward Difference 29.4 s 24.0 s Step Response Invariance 2.8 s 29.4 s Bilinear Transformation 29.4 s 29.4 s

3 Rh-SPND Consistency Test Verification

Mature application of SPNDs in nuclear power plants necessitates rigorous in-pile irradiation testing. Consistency represents a critical indicator for SPND deployment, essential for accurate core flux monitoring and safe reactor operation. To evaluate the sensitivity and consistency of a manufactured batch of SPNDs, tests were conducted in the MJTR #6 channel—a pressure tube channel isolated from the reactor cooling water, maintained at atmospheric pressure with deionized water inside, and featuring a diameter of Φ125×3 mm.

3.1 Detector Arrangement

To determine Rh-SPND neutron sensitivity, the test configuration collected Rh-SPND output signal currents while simultaneously measuring thermal neutron flux at the detector probe locations using the activation method, enabling calculation of the corresponding Rh-SPND sensitivity.

The radial arrangement of Rh-SPNDs and activation detectors is shown in FIGURE:7, with activation detectors and Rh-SPNDs positioned symmetrically along the central axis. Specifically, activation detectors were placed at the radial center and four symmetric outer positions (totaling five locations), while Rh-SPND probes were positioned at four symmetric inner radial locations. K11 faced the reactor core direction, with SPNDs #1 and #2 placed on the sunny side and SPNDs #3 and #4 on the shady side (sunny side indicates core-facing positions, shady side indicates core-opposite positions). Activation foils at positions T4, T5, T6, and T7 consisted of CoAl, while position T1 contained five detector types: CoAl, ScAl, AgAl, AuAl, and Fe.

The axial positioning of activation detectors relative to Rh-SPNDs is illustrated in FIGURE:7. Activation detectors at the radial center were distributed along upper, middle, and lower axial positions to cover the Rh-SPND length, with multiple material types at the center position and single detectors at the upper and lower positions. The four outer positions each housed one activation detector aligned with the Rh-SPND sensitive element mid-plane.

To ensure precise characterization of thermal neutron flux at Rh-SPND probe locations—such that the ratio of Rh-SPND output current to activation detector flux measurements accurately represents Rh-SPND neutron sensitivity—the radial positions of Rh-SPNDs were placed as close as possible to activation detector locations. K-type thermocouples measured Rh-SPND specimen temperatures at four radial positions matching the Rh-SPND probe holes, ensuring temperature consistency between thermocouple junctions and Rh-SPNDs.

3.2.1 Test Temperature Results

Four thermocouples (1#, 2#, 3#, 4#) measured temperatures at corresponding Rh-SPND positions. Temperature curves at different test times are shown in FIGURE:8, with detailed curves for reactor power levels of 1 MW, 2 MW, 4 MW, and 5 MW presented in FIGURE:8. As reactor power increased, core temperature rose progressively, stabilizing within the 42°C-43°C range during full-power operation (60-170 minutes).

3.2.2 Thermal Neutron Flux Activation Foil Measurement Results

To obtain absolute neutron flux at Rh-SPND locations, the irradiation assembly was removed from the reactor and disassembled. High-purity germanium gamma spectrometry measured the radioactivity of activation detector foils to determine thermal neutron flux. The dual-detector activation method (Fe and AgAl) established the thermal neutron flux at the assembly center position as 3.55×10¹² n·(cm²·s)⁻¹ (corresponding to the research reactor's full-power operation at 5 MW). Average thermal neutron flux values along the central axis are listed in [TABLE:3], while values for the four outer positions are provided in [TABLE:4]. [TABLE:5] presents the thermal neutron flux values for each of the four Rh-SPNDs, demonstrating that detectors on the sunny side measured higher flux than those on the shady side, with flux increasing closer to the core.

TABLE:3 Average Thermal Neutron Flux Along Assembly Central Axis

Activation Detector ID Position① Specific Activity at End of Irradiation (Bq·mg⁻¹) Relative Specific Activity Ratio Average Thermal Neutron Flux Along Central Axis (×10¹² n·cm⁻²·s⁻¹) CoAl-1 Upper 664.20±42.50 0.99 3.53±0.23 CoAl-2 Middle 645.10±41.30 1.00 3.53±0.23 CoAl-3 Lower 672.20±43.00 1.02 3.53±0.23

Note: ① Positions indicate upper, middle, and lower axial locations; the absolute thermal neutron flux at the middle position (with multiple detectors) is 3.550×10¹² n·(cm²·s)⁻¹ (corresponding to MJTR full-power operation at 5 MW).

TABLE:4 Average Thermal Neutron Flux for Outer Detector Corresponding Axes

Activation Detector ID Position Specific Activity at End of Irradiation (Bq·mg⁻¹) Corresponding Axis Average Thermal Neutron Flux② (×10¹² n·cm⁻²·s⁻¹) CoAl-1 Outer-1 664.20±42.50 3.71±0.24 CoAl-4 Outer-2 645.10±41.30 3.72±0.24 CoAl-5 Outer-3 672.20±43.00 3.42±0.22 CoAl-6 Outer-4 672.20±43.00 3.45±0.22

Note: ② Calculated using the central axis average thermal neutron flux of 3.530×10¹² n·cm⁻²·s⁻¹ multiplied by the corresponding position activity ratio.

TABLE:5 Thermal Neutron Flux Values at SPND Positions

SPND ID Activation Detector Position Corresponding Axis Average Thermal Neutron Flux (×10¹² n·cm⁻²·s⁻¹) SPND Position Thermal Neutron Flux Value (×10¹² n·cm⁻²·s⁻¹) 1# Outer-1 axis 3.53±0.23 3.71±0.24 2# Outer-2 axis 3.89±0.25 3.72±0.24 3# Outer-3 axis 3.92±0.25 3.42±0.22 4# Outer-4 axis 3.31±0.21 3.45±0.22

Average thermal neutron flux at four SPND positions: 3.57±0.23 ×10¹² n·cm⁻²·s⁻¹

3.2.3 Rh-SPND Sensitive Current Measurement Test Results

Online measurement and recording during irradiation yielded sensitive current outputs for Rh-SPNDs #1, #2, and #4 (#3 was damaged). The measured sensitive current curves for power levels from 1 MW to 5 MW are shown in [FIGURE:9]. The output currents of SPNDs #1 and #2 exceeded that of SPND #4 because #1 and #2 were positioned on the sunny side where neutron flux is higher, while #3 and #4 were placed on the shady side with lower neutron flux.

3.2.4 Neutron Sensitivity Test Results

Based on the neutron sensitivity definition in equation (1) and using the measured Rh-SPND signal currents together with the thermal neutron flux at full power, the neutron sensitivity values were calculated as presented in [TABLE:6]. SPNDs #1 and #2 exhibited good consistency with a deviation of only 0.63%. However, comparing all three SPNDs yields a larger consistency deviation of 6.5%, primarily due to the significantly lower sensitivity of SPND #4 compared to #1 and #2. Preliminary analysis suggests that manufacturing process issues, such as welding defects causing emitter material deficiency, resulted in the lower signal current and consequently reduced sensitivity of SPND #4.

TABLE:6 SPND Thermal Neutron Sensitivity Test Results

Detector ID Sensitivity Average Value (×10⁻²⁰ A·(n·cm⁻²·s⁻¹)⁻¹) Thermal Neutron Sensitivity (×10⁻²⁰ A·(n·cm⁻²·s⁻¹)⁻¹) 1# 1.66±0.06 1.66±0.06 2# 1.68±0.06 1.68±0.06 4# 1.44±0.06 1.44±0.06 Average 1.59±0.06 1.59±0.06

4 Conclusions

(1) Through the development of weak current amplification circuitry and algorithmic processing of delayed signals, a fast-response Rh-SPND system was successfully developed, reducing the detector's signal response time from several hundred seconds to approximately 3 seconds.

(2) During high-power operation (5 MW) in the MJTR, the test section temperature reached 42.4°C. The Rh-SPNDs demonstrated sensitive current outputs that varied consistently with reactor power across the 1 MW to 5 MW range. The average neutron sensitivity achieved 1.59×10⁻²⁰/A·(n·cm⁻²·s⁻¹)⁻¹, with good consistency observed among SPNDs from the same production batch.

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